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Question

(C) Let the total time be $t$ and acceleration be $a$. The initial velocity $u = 0$.For the first half of the time,$t_{1} = t/2$:$x_{1} = u t_{1} + \f

Vedclass · Accepted Answer

$x_{2} = 3x_{1}$

Vedclass · Answer

(C) Let the total time be $t$ and acceleration be $a$. The initial velocity $u = 0$.For the first half of the time,$t_{1} = t/2$:$x_{1} = u t_{1} + \frac{1}{2} a t_{1}^{2} = 0 + \frac{1}{2} a (t/2)^{2} = \frac{1}{8} a t^{2}$.For the total time $t$,the total distance $x_{total} = x_{1} + x_{2} = \frac{1}{2} a t^{2}$.Substituting $x_{1} = \frac{1}{8} a t^{2}$ into the total distance equation:$\frac{1}{8} a t^{2} + x_{2} = \frac{1}{2} a t^{2}$.$x_{2} = \frac{1}{2} a t^{2} - \frac{1}{8} a t^{2} = \frac{4-1}{8} a t^{2} = \frac{3}{8} a t^{2}$.Comparing $x_{1}$ and $x_{2}$:$x_{2} = 3 	imes (\frac{1}{8} a t^{2}) = 3 x_{1}$.

$A$ body starts from rest and moves with constant acceleration for $t$ seconds. It travels a distance $x_{1}$ in the first half of the time and $x_{2}$ in the next half of the time. Then:

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